Plumbene on a Magnetic Substrate: a Combined STM and DFT Study

Plumbene on a magnetic substrate: a combined STM and DFT study

Gustav Bihlmayer,1, ∗ Jonas Sassmannshausen,2 AndréKubetzka,2 Stefan Blügel,1 Kirsten von Bergmann,2, † and Roland Wiesendanger2 1Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich& JARA, 52425 Jülich, Germany 2Department of Physics, University of Hamburg, D-20355 Hamburg, Germany (Dated: June 26, 2020) As heavy analog of graphene, plumbene is a two-dimensional material with strong spin-orbit coupling effects. Using scanning tunneling microscopy (STM), we observe that Pb forms a flat honeycomb lattice on an Fe monolayer on Ir(111). In contrast, without the Fe layer, a c(2×4) structure of Pb on Ir(111) is found. We use density functional theory (DFT) calculations to rationalize these findings and analyze the impact of the hybridization on the plumbene band structure. In the unoc- cupied states the splitting of the Dirac cone by spin-orbit interaction is clearly observed while in the occupied states of the freestanding plumbene we find a band inversion that leads to the formation of a topologically non-trivial gap. Exchange splitting as mediated by the strong hybridization with the Fe layer drives a quantum spin Hall to quantum anomalous Hall state transition.

Since the exotic properties of graphene have been ture but without band inversion near the Fermi level [13]. discovered about 15 years ago [1], the field of two- Electronically it is similar to a Bi(111) bilayer with less dimensional materials in general and honeycomb struc- electrons (ZBi = 83, ZPb = 82). DFT studies suggested tures in particular has seen a dramatic increase in pop- that doping or chemical modification of plumbene [14] ularity [2]. Topological properties in these lattices de- might be necessary to achieve topological effects. Maybe pend significantly on the strength of spin-orbit coupling it is because of these findings that the quest for plumbene (SOC) effects that are notoriously small in graphene, es- has not really started yet. pecially at the K point [3]. Therefore, although the quan- Using scanning tunneling microscopy (STM) and DFT tum spin Hall effect (QSHE) was first theoretically pre- we show in this Letter that (i) using an appropriate sub- dicted for graphene [4], experimentally it was first ver- strate it is possible to form a flat plumbene lattice and (ii) ified in materials containing heavy elements like HgTe that the electronic properties of ’flat plumbene’ are rather quantum wells [5]. Since then, numerous studies have fo- exciting: Calculations predict a band-inversion in the va- cused on the synthesis and properties of heavier analogs lence bands that leads to topologically protected edge of graphene like silicene [6], germanene [7] or stanene states. Further (iii), on the ferromagnetic substrate that (Sn) [8]. But the formation of double bonds in this se- enables the formation of plumbene the induced exchange ries seems to be restricted to the carbon-based material splitting drives this feature into a quantum anomalous only and freestanding heavier analogs are considered un- Hall gap. Such exchange coupling opens the way to real- likely to form [9]. Consequently, the first silicene was ize a quantum Hall effect without external magnetic field, reported as adlayer on Ag(111) [10] and it is still challeng- a phenomenon envisioned theoretically in the eighties [15] ing to balance the interaction with the substrate required and only recently realized experimentally [16] at very low for formation with the electronic independence neces- temperatures. sary to study the topological properties via electronic We have deposited sub-monolayer amounts of Pb onto transport effects [6]. Furthermore, all heavier analogs a sample with extended Fe monolayer areas on an Ir(111) of graphene have a tendency to pronounced buckling of single crystal surface, see overview STM image in Fig. 1. their honeycomb structures, resulting in severe changes Because we observed severe intermixing of Pb and Fe of the electronic properties as compared to the ideal flat for Pb growth at room temperature we have cooled the structures [11]. Therefore, it came recently as a welcome Fe/Ir(111) to about 140 K prior to the Pb deposition [17], surprise that stanene was observed to grow on Cu(111) which results in large and well-ordered patches of Pb as a flat honeycomb lattice [12]. Despite the metallic both on the bare Ir(111) and the Fe-covered Ir(111), see arXiv:2006.14516v1 [cond-mat.mtrl-sci] 25 Jun 2020 substrate, a topological edge state could be observed on labels for the different layers in Fig. 1. The Fe mono- these islands - although 1.3 eV below the Fermi level. layer grows pseudomorphically in fcc stacking on the In this quest for heavy honeycomb structures the Pb Ir(111) substrate and in this spin-polarized STM mea- analog, plumbene, appeared relatively late on the scien- surement [18] the observed roughly square superstruc- tific stage. Isoelectronic in its valence shell with C, Si, ture with a periodicity of about 1 nm originates from the Ge and Sn it is the heaviest graphene analog and ex- magnetic nanoskyrmion lattice [19]. No magnetic signal pected to show the most pronounced SOC effects [11]. has been observed on the Pb monolayers. Density functional theory (DFT) studies of plumbene A closer view on the Pb deposited directly on the Ir and predicted the formation of a buckled honeycomb struc- on Fe/Ir is shown in Figs. 2(a) and (b), respectively. Here 2

FIG. 1. Pseudo 3-dimensional STM image of a sample of Pb FIG. 2. Closer view constant-current STM images of the on Fe on Ir(111), the different exposed surfaces are labeled. Pb monolayer on (a) the bare Ir(111) surface and (b) the Fe Pb was deposited well below room temperature and grows as monolayer on Ir(111). Both the symmetry and the atomic dis- monolayer high ordered islands both on the bare Ir surface tances for the two differently ordered Pb monolayers are dif- and on the Fe monolayer on Ir. The superstructure on the ferent and the corresponding structure models are presented pseudomorphic Fe monolayer on Ir is not due to the structure in (c) and (d). The white dashed rectangle in (c) refers to but corresponds to the magnetic signal of the nanoskyrmion the primitive unit cell of the c(2 × 4) structure and the white lattice. Measurement parameters: U = +5 mV, I = 3 nA, dashed diamond in (d) marks the p(2 × 2) unit cell; blue T = 4 K, Cr-bulk tip. dashed circles mark positions that are empty for a lower atom- density configuration and occupied for a higher-atom density configuration (confer text). Measurement parameters: (a) the superstructures are of structural origin. Due to the U = +10 mV, I = 1.5 nA; (b) U = +5 mV, I = 2 nA; both large lattice mismatch of Pb and Ir, the Pb overlayers are T = 4 K, Cr-bulk tip. Information on the bias dependence is not pseudomorphic, but instead form layers with reduced provided in the supplementary information, Fig. S1. atom density. Nevertheless, the Pb superstructures are commensurate with the substrate and atoms reside at specific adsorption sites of the Ir or Fe/Ir, an indication structural unit cell of the honeycomb has lattice vec- ˚ that the Pb-substrate interaction is comparable to the √tors with a length of 5.43 A, the Pb-Pb distance is only ˚ Pb-Pb interaction. 6/3aIr =√ 3.13 A, i.e. more than 10% shorter than in fcc On Ir(111) we find a c(4 × 2) Pb overlayer that can be Pb (aPb/ 2 = 3.52 A).˚ Comparing graphene with dia- described with a rectangular unit cell, see white dashed mond a similar contraction of bond distances (1.42 A˚ vs. rectangle in Fig. 2(c), like in the graphene intercalated 1.55 A)˚ can be observed, suggesting that the Pb-Pb bond Pb films on Ir [20]. The Pb atoms all occupy the same is modified in a similar way as the C-C bond for the two adsorption sites and the Pb-Pb distances are 4.70 A˚ and different allotropes. 5.43 A˚ for the two orthogonal directions. For symmetry Using density functional theory we study the energet- reasons three rotational domains are found on a larger ics of different Pb monolayers on Ir(111) and Fe/Ir(111). scale. Based on the experimental findings we compare four pos- In contrast, on the Pb/Fe/Ir we find a honeycomb ar- sible arrangements of Pb at these surfaces: p(2 × 2) and rangement of the Pb atoms, see experimental data and c(2 × 4) unit cells (uc.) with one or two Pb atoms per corresponding structure model in Figs. 2(b),(d), i.e. the cell, i.e. the structures shown in Figs. 2(c) and (d) with Pb grows on Fe/Ir(111) in the modification of plumbene. and without the atoms at positions marked by the dashed The structural p(2 × 2) unit cell (see white dashed di- blue circle. amond) contains two Pb atoms that adsorb in a fcc Comparing fcc and hcp adsorption sites, a single Pb and a hcp site. The Pb atom density of this honey- atom on Ir(111) forming a p(2 × 2) or c(2 × 4) structure comb plumbene layer is twice that of the c(4 × 2) Pb always prefers the fcc site by 49 meV/Pb. The p(2 × 2) overlayer on Ir. Since both the Fe/Ir and the Ir(111) and c(2 × 4) arrangements differ by only 5 meV in favor surface have the same symmetry and identical atomic of the former. The fact that experimentally a c(2 × 4) distances, the difference in the Pb overlayer structures structure is observed might be related to neglected effects cannot originate from geometrical reasons. While the from the vibrational entropy or limitations of the compu- 3

areal Pb density (2 Pb/uc.) and by 44 meV over a p(2×2) arrangement with only one Pb atom per unit cell. The structural relaxation shows that the honeycomb layer is almost completely flat with a corrugation of 0.002 A.˚ In all cases we assumed a ferromagnetic order of the Fe layer. Test calculations of Fe layers with antiferromag- netic nearest neighbor interactions lead to much higher total energies (see supplementary information). A similar magnetic hardening was observed when coronene is adsorbed on the Fe/Ir(111) nanoskyrmion lattice [21] and can occur generally, when p electrons of molecules inter- act with a magnetic layer underneath [22]. To understand the radically different energetics of Pb on Ir(111) and on Fe/Ir(111) we analyze the orbitally resolved density of states (DOS) for the honeycomb structure in Fig. 3. In the case of the Fe/Ir(111) substrate, we see that the DOS of the Pb px and py states is almost degenerate and rather featureless near the Fermi level, while the pz states show characteristic peaks at or below 1 eV binding energy where the minority Fe states are located (the majority states of Fe are peaked between 2 and 3 eV binding energy, see supplementary information, Fig. S3). While in this case the in-plane and out-of-plane oriented p orbitals of Pb seem rather decoupled (as expected from a 2D structure bonded by pz orbitals to the substrate), in the Pb/Ir(111) case we find a completely different orbital arrangement with py/pz orbitals bond- ing to the Ir substrate. Although also in this case an almost flat Pb honeycomb structure is obtained, the in- volved orbitals are completely different. Therefore, it can be concluded that the hybridization with the Fe states, FIG. 3. (a) Locally and orbitally resolved DOS of the Pb that are available in the energy range of the Pb pz states, atoms in the honeycomb structure on Fe/Ir(111). The total is responsible for the formation of the 2D Pb honeycomb Pb DOS is shown as gray background, the s, px, py and pz lattice. contributions are shown in black, blue, green and red, respec- Turning now to the band structure of Pb on Fe/Ir(111), tively. Positive and negative values correspond to majority and minority spins, respectively. (b) The same quantities for it is instructive to investigate first the plumbene layer the Pb honeycomb lattice on Ir(111). without the substrate (black lines in Fig. 4). Below the Fermi level two rather flat bands can be found and the pz states form a hole pocket around the K point, compen- sated by a shallow electron pocket of the antibonding px,y tational method. To put two Pb atoms into a c(2×4) uc., states at Γ. At around 1 eV binding energy the bond- however, requires 54 meV/Pb more energy than a single ing px,y states show a band inversion with the pz states one and the formation of a Pb honeycomb lattice in the at the Γ point, very similar to the band inversion ob- p(2 × 2) cell is energetically 216 meV/Pb more expensive served for stanene in Ref. [12]. On the metallic substrate than the c(2 × 4) arrangement with the same atom den- these Pb states are, however, strongly hybridized with sity. Thus, on Ir(111) a low Pb atom density with larger the Fe d states and –as evident from Fig. 4– only above Pb-Pb distances is energetically favorable as found in the the Fermi level the individual Pb states can be identified experiments reported here and in the graphene covered again. The induced spin-splitting in these states is sub- system [20]. Our STM simulations based on the local stantial, between 0.2 and 0.4 eV. This can be seen best density of states (LDOS) also show good agreement with at the K point, where the Dirac-type band crossing is the experimental images (see supplementary information, lifted by SOC (for the band structure without SOC see Fig. S2). supplementary information, Fig. S4. This high energy cost to form a Pb honeycomb struc- Although the features of the Pb bands are blurred by ture on Ir(111) is contrasted by the energetics of Pb on hybridization, it is of interest to study the consequences Fe/Ir(111): here the honeycomb lattice is favored by 11 of the above-mentioned band inversion of plumbene at meV/Pb atom over the c(2 × 4) structure with the same the Γ point. Strong SOC in Pb opens a 150 meV band 4

the calculation that reproduces the spin-splitting of the Pb bands seen in Fig. 4. Although in the projection on the edge the spin-split band-edges now overlap, the single, spin-polarized edge channel is clearly visible in this system (Fig. 5). We have shown experimental and theoretical evi- dence that the heaviest member of the graphene fam- ily, plumbene, can be prepared on an Fe layer on Ir(111). Selective hybridization of the Pb pz states with the Fe minority d states stabilize the honeycomb structure, while on bare Ir(111) a rectangular c(2 × 4) Pb layer is formed. The ferromagnetic substrate induces a signiﬁcant exchange splitting in the plumbene. Freestanding plumbene with this lattice constant shows a band-inversion in the occupied states and topologi- FIG. 4. Red/blue: spin polarization of the Pb states of a Pb cally protected edge states. With the exchange splitting honeycomb structure on Fe/Ir(111). Spin-orbit coupling is in- this quantum-spin-Hall gap is changed into a quantum- cluded and the spin-quantization axis is assumed to be normal anomalous-Hall gap providing a protected charge chan- to the surface. In black the band structure of a freestanding nel. Although on the metallic substrate these states will plumbene layer with the same structure as the deposited one be considerably broadened and not accessible to trans- is shown. port measurements, with a modiﬁed substrate this system might be a nice platform to study the properties of edge states of a Chern insulator.

ACKNOWLEDGMENTS

We would like to thank Niklas Romming for techni- cal assistance with the experiments. We gratefully ac- knowledge the Collaborative Research Center SPP 1666 of the Deutsche Forschungsgemeinschaft (DFG) and the computing time on the JURECA supercomputer of the Jlich Supercomputing Centre (JSC). Financial support from the ERC Advanced Grant ADMIRE is gratefully acknowledged.

FIG. 5. (a) Band structure of an edge-hydrogenated plumbene ribbon in an external magnetic field. The size of the dots marks the weight of the states on one of the zig-zag edges, the color indicates the spin character. (b) Constant- ∗ [email protected] current STM image of the typical zigzag configuration of the † [email protected] edge of a plumbene island on Fe/Ir; measurement parameters: [1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, U = −10 mV, I = 2 nA, T = 4 K, Cr-bulk tip. Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science 306, 666 (2004). [2] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. gap between the states that hosts topologically protected Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009). edge states. In the calculation of the edge-hydrogenated [3] C.-C. Liu, W. Feng, and Y. Yao, Phys. Rev. Lett. 107, plumbene zig-zag ribbon the linear dispersion of the edge 076802 (2011). state is clearly visible in the gap (see supplementary in- [4] C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 formation, Fig. S5). This is a clear signature of the quan- (2005). tum spin Hall effect (although in the occupied states) as [5] M. König,S. Wiedmann, C. Brüne,A. Roth, H. Buh- expected from the parity analysis of the bands. Since mann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, the Fe substrate induces a strong exchange field in the Science 318, 766 (2007). [6] A. Molle, C. Grazianetti, L. Tao, D. Taneja, M. H. Alam, plumbene, we can further look for the appearance of a and D. Akinwande, Chem. Soc. Rev. 47, 6370 (2018). quantum anomalous Hall gap in the system. To simu- [7] L. Zhang, P. Bampoulis, A. N. Rudenko, Q. Yao, A. van late the effect of the exchange field in the unsupported Houselt, B. Poelsema, M. I. Katsnelson, and H. J. W. plumbene ribbon, we add an external magnetic field in Zandvliet, Phys. Rev. Lett. 116, 256804 (2016). 5

[8] F.-F. Zhu, W.-J. Chen, Y. Xu, C.-L. Gao, D.-D. Guan, [16] C.-Z. Chang, J. Zhang, X. Feng, J. Shen, Z. Zhang, C.-H. Liu, D. Qian, S.-C. Zhang, and J.-F. Jia, Nature M. Guo, K. Li, Y. Ou, P. Wei, L.-L. Wang, Z.-Q. Ji, Mater. 14, 1020 (2015). Y. Feng, S. Ji, X. Chen, J. Jia, X. Dai, Z. Fang, S.-C. [9] R. Hoffmann, Angew. Chem. Int. Ed. 52, 93 (2013). Zhang, K. He, Y. Wang, L. Lu, X.-C. Ma, and Q.-K. [10] P. Vogt, P. De Padova, C. Quaresima, J. Avila, Xue, Science 340, 167 (2013). E. Frantzeskakis, M. C. Asensio, A. Resta, B. Ealet, and [17] J. Sassmannshausen, A. Kubetzka, P.-J. Hsu, K. von G. Le Lay, Phys. Rev. Lett. 108, 155501 (2012). Bergmann, and R. Wiesendanger, Phys. Rev. B 98, [11] Z.-Q. Huang, C.-H. Hsu, F.-C. Chuang, Y.-T. Liu, 144443 (2018). H. Lin, W.-S. Su, V. Ozolins, and A. Bansil, New Journal [18] R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009). of Physics 16, 105018 (2014). [19] S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Ku- [12] J. Deng, B. Xia, X. Ma, H. Chen, H. Shan, X. Zhai, B. Li, betzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, A. Zhao, Y. Xu, W. Duan, S.-C. Zhang, B. Wang, and Nature Phys. 7, 713 (2011). J. G. Hou, Nature Mater. 17, 1081 (2018). [20] F. Calleja, H. Ochoa, M. Garnica, S. Barja, J. J. Navarro, [13] X.-L. Yu, L. Huang, and J. Wu, Phys. Rev. B 95, 125113 A. Black, M. M. Otrokov, E. V. Chulkov, A. Arnau, (2017). A. L. V. de Parga, F. Guinea, and R. Miranda, Nature [14] H. Zhao, C.-W. Zhang, W.-X. Ji, R.-W. Zhang, S.-S. Phys. 11, 43 (2015). Li, S.-S. Yan, B.-M. Zhang, P. Li, and P.-J. Wang, Sci. [21] J. Brede, N. Atodiresei, V. Caciuc, M. Bazarnik, A. Al- Reports 6, 20152 (2016). Zubi, S. Blügel,and R. Wiesendanger, Nature Nanotech- [15] F. D. M. Haldane, Phys. Rev. Lett. 61, 2015 (1988). nology 9, 1018 (2014). [22] R. Friedrich, V. Caciuc, N. S. Kiselev, N. Atodiresei, and S. Blügel,Phys. Rev. B 91, 115432 (2015).